%------------------------------------------------------------------------------
% File : FindProof---0.1
% Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% Transfm : none
% Format : tptp:raw
% Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 02:11:34 PM UTC 2026
% Result : Unsatisfiable 19.94s 3.64s
% Output : Proof 19.94s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 24
% Syntax : Number of formulae : 144 ( 32 unt; 0 def)
% Number of atoms : 403 ( 15 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 510 ( 251 ~; 259 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-4 aty)
% Number of functors : 11 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 188 ( 0 sgn 80 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
cnf(f20,axiom,
( greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_relationship_of_growth_rates_53) ).
fof(f20_nnf,plain,
! [A,B] :
( greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f20]) ).
fof(f20_sk,plain,
! [A,B] :
( greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| greater(zero,difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f20_nnf]) ).
cnf(c20,plain,
( greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| greater(zero,difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f20_sk]) ).
cnf(f25,negated_conjecture,
environment(sk1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_58) ).
fof(f25_nnf,plain,
environment(sk1),
inference(nnf_transformation,[status(thm)],[f25]) ).
cnf(c25,plain,
environment(sk1),
inference(cnf_transformation,[status(esa)],[f25_nnf]) ).
cnf(p73,plain,
( greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c20,c25]) ).
cnf(f2,axiom,
( subpopulations(first_movers,efficient_producers,A,critical_point(A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_point_means_FM_and_EP_35) ).
fof(f2_nnf,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,A,critical_point(A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f2]) ).
fof(f2_sk,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,A,critical_point(A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f2_nnf]) ).
cnf(c2,plain,
( subpopulations(first_movers,efficient_producers,X0,critical_point(X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f2_sk]) ).
cnf(p35,plain,
( subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1))
| ~ in_environment(sk1,critical_point(sk1)) ),
inference(resolution,[status(thm)],[c2,c25]) ).
cnf(f26,negated_conjecture,
in_environment(sk1,critical_point(sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_59) ).
fof(f26_nnf,plain,
in_environment(sk1,critical_point(sk1)),
inference(nnf_transformation,[status(thm)],[f26]) ).
cnf(c26,plain,
in_environment(sk1,critical_point(sk1)),
inference(cnf_transformation,[status(esa)],[f26_nnf]) ).
cnf(p36,plain,
subpopulations(first_movers,efficient_producers,sk1,critical_point(sk1)),
inference(resolution,[status(thm)],[p35,c26]) ).
cnf(p134,plain,
( greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) ),
inference(resolution,[status(thm)],[p73,p36]) ).
cnf(f5,axiom,
( greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero)
| ~ decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)))
| ~ greater(B,C)
| ~ greater_or_equal(C,appear(efficient_producers,A))
| ~ greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_decreasing_function_38) ).
fof(f5_nnf,plain,
! [A,B,C] :
( greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero)
| ~ decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)))
| ~ greater(B,C)
| ~ greater_or_equal(C,appear(efficient_producers,A))
| ~ greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f5]) ).
fof(f5_sk,plain,
! [A,B,C] :
( greater(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)),zero)
| ~ decreases(difference(growth_rate(first_movers,C),growth_rate(efficient_producers,C)))
| ~ greater(B,C)
| ~ greater_or_equal(C,appear(efficient_producers,A))
| ~ greater_or_equal(difference(growth_rate(first_movers,B),growth_rate(efficient_producers,B)),zero)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f5_nnf]) ).
cnf(c5,plain,
( greater(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)),zero)
| ~ decreases(difference(growth_rate(first_movers,X2),growth_rate(efficient_producers,X2)))
| ~ greater(X1,X2)
| ~ greater_or_equal(X2,appear(efficient_producers,X0))
| ~ greater_or_equal(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f5_sk]) ).
cnf(p44,plain,
( greater(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)),zero)
| ~ decreases(difference(growth_rate(first_movers,X1),growth_rate(efficient_producers,X1)))
| ~ greater(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sk1))
| ~ greater_or_equal(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c5,c25]) ).
cnf(p47,plain,
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ greater(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ greater_or_equal(difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1))),zero) ),
inference(resolution,[status(thm)],[p44,c26]) ).
cnf(p165,plain,
( greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero)
| ~ decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| ~ greater(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) ),
inference(resolution,[status(thm)],[p134,p47]) ).
cnf(f27,negated_conjecture,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_60) ).
fof(f27_nnf,plain,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
inference(nnf_transformation,[status(thm)],[f27]) ).
cnf(c27,plain,
greater_or_equal(sk2,appear(efficient_producers,sk1)),
inference(cnf_transformation,[status(esa)],[f27_nnf]) ).
cnf(p191,plain,
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| ~ greater(critical_point(sk1),sk2)
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) ),
inference(resolution,[status(thm)],[p165,c27]) ).
cnf(f28,negated_conjecture,
greater(critical_point(sk1),sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_61) ).
fof(f28_nnf,plain,
greater(critical_point(sk1),sk2),
inference(nnf_transformation,[status(thm)],[f28]) ).
cnf(c28,plain,
greater(critical_point(sk1),sk2),
inference(cnf_transformation,[status(esa)],[f28_nnf]) ).
cnf(p219,plain,
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| ~ decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) ),
inference(resolution,[status(thm)],[p191,c28]) ).
cnf(f23,hypothesis,
( subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(C,D)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a10_56) ).
fof(f23_nnf,plain,
! [A,B,C,D] :
( subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(C,D)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f23]) ).
fof(f23_sk,plain,
! [A,B,C,D] :
( subpopulations(first_movers,efficient_producers,A,D)
| ~ greater_or_equal(C,D)
| ~ greater_or_equal(D,B)
| ~ subpopulations(first_movers,efficient_producers,A,C)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f23_nnf]) ).
cnf(c23,plain,
( subpopulations(first_movers,efficient_producers,X0,X3)
| ~ greater_or_equal(X2,X3)
| ~ greater_or_equal(X3,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X2)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f23_sk]) ).
cnf(p87,plain,
( subpopulations(first_movers,efficient_producers,sk1,X2)
| ~ greater_or_equal(X1,X2)
| ~ greater_or_equal(X2,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c23,c25]) ).
cnf(f13,axiom,
( in_environment(A,B)
| ~ greater(critical_point(A),B)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_critical_time_points_46) ).
fof(f13_nnf,plain,
! [A,B] :
( in_environment(A,B)
| ~ greater(critical_point(A),B)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f13]) ).
fof(f13_sk,plain,
! [A,B] :
( in_environment(A,B)
| ~ greater(critical_point(A),B)
| ~ greater_or_equal(B,appear(efficient_producers,A))
| ~ in_environment(A,critical_point(A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f13_nnf]) ).
cnf(c13,plain,
( in_environment(X0,X1)
| ~ greater(critical_point(X0),X1)
| ~ greater_or_equal(X1,appear(efficient_producers,X0))
| ~ in_environment(X0,critical_point(X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f13_sk]) ).
cnf(p65,plain,
( in_environment(sk1,X0)
| ~ greater(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ in_environment(sk1,critical_point(sk1)) ),
inference(resolution,[status(thm)],[c13,c25]) ).
cnf(p74,plain,
( in_environment(sk1,X0)
| ~ greater(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p65,c26]) ).
cnf(f19,axiom,
( greater_or_equal(A,B)
| A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_52) ).
fof(f19_nnf,plain,
! [A,B] :
( greater_or_equal(A,B)
| A != B ),
inference(nnf_transformation,[status(thm)],[f19]) ).
fof(f19_sk,plain,
! [A,B] :
( greater_or_equal(A,B)
| A != B ),
inference(skolemisation,[status(esa)],[f19_nnf]) ).
cnf(c19,plain,
( greater_or_equal(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f19_sk]) ).
cnf(p34,plain,
greater_or_equal(X0,X0),
inference(equality_resolution,[status(thm)],[c19]) ).
cnf(p76,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p74,p34]) ).
cnf(f16,axiom,
( greater_or_equal(B,appear(efficient_producers,A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_members_EP_appeared_49) ).
fof(f16_nnf,plain,
! [A,B] :
( greater_or_equal(B,appear(efficient_producers,A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f16]) ).
fof(f16_sk,plain,
! [A,B] :
( greater_or_equal(B,appear(efficient_producers,A))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f16_nnf]) ).
cnf(c16,plain,
( greater_or_equal(X1,appear(efficient_producers,X0))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f16_sk]) ).
cnf(p49,plain,
( greater_or_equal(X0,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c16,c25]) ).
cnf(p50,plain,
greater_or_equal(critical_point(sk1),appear(efficient_producers,sk1)),
inference(resolution,[status(thm)],[p49,p36]) ).
cnf(f17,axiom,
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_50) ).
fof(f17_nnf,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(nnf_transformation,[status(thm)],[f17]) ).
fof(f17_sk,plain,
! [A,B] :
( A = B
| greater(A,B)
| ~ greater_or_equal(A,B) ),
inference(skolemisation,[status(esa)],[f17_nnf]) ).
cnf(c17,plain,
( X0 = X1
| greater(X0,X1)
| ~ greater_or_equal(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f17_sk]) ).
cnf(p51,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| greater(critical_point(sk1),appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p50,c17]) ).
cnf(p88,plain,
( critical_point(sk1) = appear(efficient_producers,sk1)
| in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p76,p51]) ).
cnf(p75,plain,
( in_environment(sk1,sk2)
| ~ greater(critical_point(sk1),sk2) ),
inference(resolution,[status(thm)],[p74,c27]) ).
cnf(p79,plain,
in_environment(sk1,sk2),
inference(resolution,[status(thm)],[p75,c28]) ).
cnf(f10,axiom,
( in_environment(A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(C,D)
| ~ in_environment(A,C)
| ~ in_environment(A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_durations_are_time_intervals_43) ).
fof(f10_nnf,plain,
! [A,B,C,D] :
( in_environment(A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(C,D)
| ~ in_environment(A,C)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
fof(f10_sk,plain,
! [A,B,C,D] :
( in_environment(A,D)
| ~ greater_or_equal(D,B)
| ~ greater_or_equal(C,D)
| ~ in_environment(A,C)
| ~ in_environment(A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f10_nnf]) ).
cnf(c10,plain,
( in_environment(X0,X3)
| ~ greater_or_equal(X3,X1)
| ~ greater_or_equal(X2,X3)
| ~ in_environment(X0,X2)
| ~ in_environment(X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f10_sk]) ).
cnf(p57,plain,
( in_environment(sk1,X2)
| ~ greater_or_equal(X2,X0)
| ~ greater_or_equal(X1,X2)
| ~ in_environment(sk1,X1)
| ~ in_environment(sk1,X0) ),
inference(resolution,[status(thm)],[c10,c25]) ).
cnf(p60,plain,
( in_environment(sk1,X1)
| ~ greater_or_equal(X1,X0)
| ~ greater_or_equal(X0,X1)
| ~ in_environment(sk1,X0) ),
inference(factoring,[status(thm)],[p57]) ).
cnf(p82,plain,
( in_environment(sk1,X0)
| ~ greater_or_equal(X0,sk2)
| ~ greater_or_equal(sk2,X0) ),
inference(resolution,[status(thm)],[p79,p60]) ).
cnf(p85,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater_or_equal(appear(efficient_producers,sk1),sk2) ),
inference(resolution,[status(thm)],[p82,c27]) ).
cnf(p95,plain,
( in_environment(sk1,appear(efficient_producers,sk1))
| ~ greater_or_equal(critical_point(sk1),sk2)
| in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(superposition,[status(thm)],[p88,p85]) ).
cnf(p121,plain,
( ~ greater_or_equal(critical_point(sk1),sk2)
| in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(factoring,[status(thm)],[p95]) ).
cnf(f18,axiom,
( greater_or_equal(A,B)
| ~ greater(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_greater_or_equal_51) ).
fof(f18_nnf,plain,
! [A,B] :
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(nnf_transformation,[status(thm)],[f18]) ).
fof(f18_sk,plain,
! [A,B] :
( greater_or_equal(A,B)
| ~ greater(A,B) ),
inference(skolemisation,[status(esa)],[f18_nnf]) ).
cnf(c18,plain,
( greater_or_equal(X0,X1)
| ~ greater(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f18_sk]) ).
cnf(p33,plain,
greater_or_equal(critical_point(sk1),sk2),
inference(resolution,[status(thm)],[c18,c28]) ).
cnf(p122,plain,
in_environment(sk1,appear(efficient_producers,sk1)),
inference(resolution,[status(thm)],[p121,p33]) ).
cnf(f3,axiom,
( subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A))
| ~ in_environment(A,appear(efficient_producers,A))
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_FM_and_EP_when_EP_appears_36) ).
fof(f3_nnf,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A))
| ~ in_environment(A,appear(efficient_producers,A))
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f3]) ).
fof(f3_sk,plain,
! [A] :
( subpopulations(first_movers,efficient_producers,A,appear(efficient_producers,A))
| ~ in_environment(A,appear(efficient_producers,A))
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f3_nnf]) ).
cnf(c3,plain,
( subpopulations(first_movers,efficient_producers,X0,appear(efficient_producers,X0))
| ~ in_environment(X0,appear(efficient_producers,X0))
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f3_sk]) ).
cnf(p39,plain,
( subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1))
| ~ in_environment(sk1,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[c3,c25]) ).
cnf(p123,plain,
subpopulations(first_movers,efficient_producers,sk1,appear(efficient_producers,sk1)),
inference(resolution,[status(thm)],[p122,p39]) ).
cnf(p149,plain,
( subpopulations(first_movers,efficient_producers,sk1,X1)
| ~ greater_or_equal(X0,X1)
| ~ greater_or_equal(X1,appear(efficient_producers,sk1))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[p87,p123]) ).
cnf(p151,plain,
( subpopulations(first_movers,efficient_producers,sk1,X0)
| ~ greater_or_equal(critical_point(sk1),X0)
| ~ greater_or_equal(X0,appear(efficient_producers,sk1)) ),
inference(resolution,[status(thm)],[p149,p36]) ).
cnf(p152,plain,
( subpopulations(first_movers,efficient_producers,sk1,sk2)
| ~ greater_or_equal(critical_point(sk1),sk2) ),
inference(resolution,[status(thm)],[p151,c27]) ).
cnf(p153,plain,
subpopulations(first_movers,efficient_producers,sk1,sk2),
inference(resolution,[status(thm)],[p152,p33]) ).
cnf(f24,hypothesis,
( decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a12_57) ).
fof(f24_nnf,plain,
! [A,B] :
( decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f24]) ).
fof(f24_sk,plain,
! [A,B] :
( decreases(difference(founding_rate(first_movers,B),founding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f24_nnf]) ).
cnf(c24,plain,
( decreases(difference(founding_rate(first_movers,X1),founding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f24_sk]) ).
cnf(p55,plain,
( decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c24,c25]) ).
cnf(p157,plain,
decreases(difference(founding_rate(first_movers,sk2),founding_rate(efficient_producers,sk2))),
inference(resolution,[status(thm)],[p153,p55]) ).
cnf(f4,axiom,
( decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_difference_between_founding_rates_37) ).
fof(f4_nnf,plain,
! [A] :
( decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))) ),
inference(nnf_transformation,[status(thm)],[f4]) ).
fof(f4_sk,plain,
! [A] :
( decreases(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)))
| decreases(difference(disbanding_rate(first_movers,A),disbanding_rate(efficient_producers,A)))
| ~ decreases(difference(founding_rate(first_movers,A),founding_rate(efficient_producers,A))) ),
inference(skolemisation,[status(esa)],[f4_nnf]) ).
cnf(c4,plain,
( decreases(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)))
| decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ decreases(difference(founding_rate(first_movers,X0),founding_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[status(esa)],[f4_sk]) ).
cnf(p167,plain,
( decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)))
| decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))) ),
inference(resolution,[status(thm)],[p157,c4]) ).
cnf(f1,axiom,
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_34) ).
fof(f1_nnf,plain,
! [A,B] :
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f1]) ).
fof(f1_sk,plain,
! [A,B] :
( ~ decreases(difference(disbanding_rate(first_movers,B),disbanding_rate(efficient_producers,B)))
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f1_nnf]) ).
cnf(c1,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X1),disbanding_rate(efficient_producers,X1)))
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f1_sk]) ).
cnf(p32,plain,
( ~ decreases(difference(disbanding_rate(first_movers,X0),disbanding_rate(efficient_producers,X0)))
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c1,c25]) ).
cnf(p155,plain,
~ decreases(difference(disbanding_rate(first_movers,sk2),disbanding_rate(efficient_producers,sk2))),
inference(resolution,[status(thm)],[p153,p32]) ).
cnf(p171,plain,
decreases(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))),
inference(resolution,[status(thm)],[p167,p155]) ).
cnf(p222,plain,
( greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero)
| greater(zero,difference(growth_rate(first_movers,critical_point(sk1)),growth_rate(efficient_producers,critical_point(sk1)))) ),
inference(resolution,[status(thm)],[p219,p171]) ).
cnf(f6,axiom,
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_negative_growth_rate_difference_39) ).
fof(f6_nnf,plain,
! [A] :
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) ),
inference(nnf_transformation,[status(thm)],[f6]) ).
fof(f6_sk,plain,
! [A] :
( greater(growth_rate(efficient_producers,A),growth_rate(first_movers,A))
| ~ greater(zero,difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A))) ),
inference(skolemisation,[status(esa)],[f6_nnf]) ).
cnf(c6,plain,
( greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| ~ greater(zero,difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))) ),
inference(cnf_transformation,[status(esa)],[f6_sk]) ).
cnf(p225,plain,
( greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1)))
| greater(difference(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),zero) ),
inference(resolution,[status(thm)],[p222,c6]) ).
cnf(f8,axiom,
( greater(growth_rate(first_movers,A),growth_rate(efficient_producers,A))
| ~ greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_positive_growth_rate_difference_41) ).
fof(f8_nnf,plain,
! [A] :
( greater(growth_rate(first_movers,A),growth_rate(efficient_producers,A))
| ~ greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
fof(f8_sk,plain,
! [A] :
( greater(growth_rate(first_movers,A),growth_rate(efficient_producers,A))
| ~ greater(difference(growth_rate(first_movers,A),growth_rate(efficient_producers,A)),zero) ),
inference(skolemisation,[status(esa)],[f8_nnf]) ).
cnf(c8,plain,
( greater(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0))
| ~ greater(difference(growth_rate(first_movers,X0),growth_rate(efficient_producers,X0)),zero) ),
inference(cnf_transformation,[status(esa)],[f8_sk]) ).
cnf(p227,plain,
( greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2))
| greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1))) ),
inference(resolution,[status(thm)],[p225,c8]) ).
cnf(f21,hypothesis,
( ~ greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| B != critical_point(A)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_54) ).
fof(f21_nnf,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| B != critical_point(A)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f21]) ).
fof(f21_sk,plain,
! [A,B] :
( ~ greater(growth_rate(efficient_producers,B),growth_rate(first_movers,B))
| B != critical_point(A)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f21_nnf]) ).
cnf(c21,plain,
( ~ greater(growth_rate(efficient_producers,X1),growth_rate(first_movers,X1))
| X1 != critical_point(X0)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f21_sk]) ).
cnf(p53,plain,
( ~ greater(growth_rate(efficient_producers,X0),growth_rate(first_movers,X0))
| X0 != critical_point(sk1) ),
inference(resolution,[status(thm)],[c21,c25]) ).
cnf(p54,plain,
~ greater(growth_rate(efficient_producers,critical_point(sk1)),growth_rate(first_movers,critical_point(sk1))),
inference(equality_resolution,[status(thm)],[p53]) ).
cnf(p230,plain,
greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)),
inference(resolution,[status(thm)],[p227,p54]) ).
cnf(f15,axiom,
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp_symmetry_of_subpopulations_48) ).
fof(f15_nnf,plain,
! [A,B] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f15]) ).
fof(f15_sk,plain,
! [A,B] :
( subpopulations(efficient_producers,first_movers,A,B)
| ~ subpopulations(first_movers,efficient_producers,A,B)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f15_nnf]) ).
cnf(c15,plain,
( subpopulations(efficient_producers,first_movers,X0,X1)
| ~ subpopulations(first_movers,efficient_producers,X0,X1)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f15_sk]) ).
cnf(p43,plain,
( subpopulations(efficient_producers,first_movers,sk1,X0)
| ~ subpopulations(first_movers,efficient_producers,sk1,X0) ),
inference(resolution,[status(thm)],[c15,c25]) ).
cnf(p156,plain,
subpopulations(efficient_producers,first_movers,sk1,sk2),
inference(resolution,[status(thm)],[p153,p43]) ).
cnf(f0,axiom,
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mp1_high_growth_rates_33) ).
fof(f0_nnf,plain,
! [A,B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(nnf_transformation,[status(thm)],[f0]) ).
fof(f0_sk,plain,
! [A,B,C,D] :
( selection_favors(C,B,D)
| ~ greater(growth_rate(C,D),growth_rate(B,D))
| ~ subpopulations(B,C,A,D)
| ~ environment(A) ),
inference(skolemisation,[status(esa)],[f0_nnf]) ).
cnf(c0,plain,
( selection_favors(X2,X1,X3)
| ~ greater(growth_rate(X2,X3),growth_rate(X1,X3))
| ~ subpopulations(X1,X2,X0,X3)
| ~ environment(X0) ),
inference(cnf_transformation,[status(esa)],[f0_sk]) ).
cnf(p30,plain,
( selection_favors(X1,X0,X2)
| ~ greater(growth_rate(X1,X2),growth_rate(X0,X2))
| ~ subpopulations(X0,X1,sk1,X2) ),
inference(resolution,[status(thm)],[c0,c25]) ).
cnf(p166,plain,
( selection_favors(first_movers,efficient_producers,sk2)
| ~ greater(growth_rate(first_movers,sk2),growth_rate(efficient_producers,sk2)) ),
inference(resolution,[status(thm)],[p156,p30]) ).
cnf(p233,plain,
selection_favors(first_movers,efficient_producers,sk2),
inference(resolution,[status(thm)],[p230,p166]) ).
cnf(f29,negated_conjecture,
~ selection_favors(first_movers,efficient_producers,sk2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_t3_62) ).
fof(f29_nnf,plain,
~ selection_favors(first_movers,efficient_producers,sk2),
inference(nnf_transformation,[status(thm)],[f29]) ).
fof(f29_sk,plain,
~ selection_favors(first_movers,efficient_producers,sk2),
inference(skolemisation,[status(esa)],[f29_nnf]) ).
cnf(c29,plain,
~ selection_favors(first_movers,efficient_producers,sk2),
inference(cnf_transformation,[status(esa)],[f29_sk]) ).
cnf(p234,plain,
$false,
inference(resolution,[status(thm)],[p233,c29]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : MGT034-2 : TPTP v9.3.1. Released v2.4.0.
% 0.00/0.03 % Command : run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.10/0.56 % Computer : n006.cluster.edu
% 0.10/0.56 % Model : x86_64 x86_64
% 0.10/0.56 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.56 % Memory : 8046.5625MB
% 0.10/0.56 % OS : Linux 6.8.0-71-generic
% 0.10/0.56 % CPULimit : 300
% 0.10/0.56 % WCLimit : 300
% 0.10/0.56 % DateTime : Thu Sep 24 01:06:59 UTC 2026
% 0.10/0.57 % CPUTime :
% 0.10/0.57 Running run_findproof /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 19.94/3.64 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 19.94/3.64 % SZS output start Proof for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
%------------------------------------------------------------------------------